OpenCV
4.5.0pre
Open Source Computer Vision

Scaling is just resizing of the image. OpenCV comes with a function cv.resize() for this purpose. The size of the image can be specified manually, or you can specify the scaling factor. Different interpolation methods are used. Preferable interpolation methods are cv.INTER_AREA for shrinking and cv.INTER_CUBIC (slow) & cv.INTER_LINEAR for zooming.
We use the function: cv.resize (src, dst, dsize, fx = 0, fy = 0, interpolation = cv.INTER_LINEAR)
src  input image 
dst  output image; it has the size dsize (when it is nonzero) or the size computed from src.size(), fx, and fy; the type of dst is the same as of src. 
dsize  output image size; if it equals zero, it is computed as: \[𝚍𝚜𝚒𝚣𝚎 = 𝚂𝚒𝚣𝚎(𝚛𝚘𝚞𝚗𝚍(𝚏𝚡*𝚜𝚛𝚌.𝚌𝚘𝚕𝚜), 𝚛𝚘𝚞𝚗𝚍(𝚏𝚢*𝚜𝚛𝚌.𝚛𝚘𝚠𝚜))\] Either dsize or both fx and fy must be nonzero. 
fx  scale factor along the horizontal axis; when it equals 0, it is computed as \[(𝚍𝚘𝚞𝚋𝚕𝚎)𝚍𝚜𝚒𝚣𝚎.𝚠𝚒𝚍𝚝𝚑/𝚜𝚛𝚌.𝚌𝚘𝚕𝚜\] 
fy  scale factor along the vertical axis; when it equals 0, it is computed as \[(𝚍𝚘𝚞𝚋𝚕𝚎)𝚍𝚜𝚒𝚣𝚎.𝚑𝚎𝚒𝚐𝚑𝚝/𝚜𝚛𝚌.𝚛𝚘𝚠𝚜\] 
interpolation  interpolation method(see cv.InterpolationFlags) 
Translation is the shifting of object's location. If you know the shift in (x,y) direction, let it be \((t_x,t_y)\), you can create the transformation matrix \(\textbf{M}\) as follows:
\[M = \begin{bmatrix} 1 & 0 & t_x \\ 0 & 1 & t_y \end{bmatrix}\]
We use the function: cv.warpAffine (src, dst, M, dsize, flags = cv.INTER_LINEAR, borderMode = cv.BORDER_CONSTANT, borderValue = new cv.Scalar())
src  input image. 
dst  output image that has the size dsize and the same type as src. 
Mat  2 × 3 transformation matrix(cv.CV_64FC1 type). 
dsize  size of the output image. 
flags  combination of interpolation methods(see cv.InterpolationFlags) and the optional flag WARP_INVERSE_MAP that means that M is the inverse transformation ( 𝚍𝚜𝚝→𝚜𝚛𝚌 ) 
borderMode  pixel extrapolation method (see cv.BorderTypes); when borderMode = BORDER_TRANSPARENT, it means that the pixels in the destination image corresponding to the "outliers" in the source image are not modified by the function. 
borderValue  value used in case of a constant border; by default, it is 0. 
rows.
Rotation of an image for an angle \(\theta\) is achieved by the transformation matrix of the form
\[M = \begin{bmatrix} cos\theta & sin\theta \\ sin\theta & cos\theta \end{bmatrix}\]
But OpenCV provides scaled rotation with adjustable center of rotation so that you can rotate at any location you prefer. Modified transformation matrix is given by
\[\begin{bmatrix} \alpha & \beta & (1 \alpha ) \cdot center.x  \beta \cdot center.y \\  \beta & \alpha & \beta \cdot center.x + (1 \alpha ) \cdot center.y \end{bmatrix}\]
where:
\[\begin{array}{l} \alpha = scale \cdot \cos \theta , \\ \beta = scale \cdot \sin \theta \end{array}\]
We use the function: cv.getRotationMatrix2D (center, angle, scale)
center  center of the rotation in the source image. 
angle  rotation angle in degrees. Positive values mean counterclockwise rotation (the coordinate origin is assumed to be the topleft corner). 
scale  isotropic scale factor. 
In affine transformation, all parallel lines in the original image will still be parallel in the output image. To find the transformation matrix, we need three points from input image and their corresponding locations in output image. Then cv.getAffineTransform will create a 2x3 matrix which is to be passed to cv.warpAffine.
We use the function: cv.getAffineTransform (src, dst)
src  three points([3, 1] size and cv.CV_32FC2 type) from input imag. 
dst  three corresponding points([3, 1] size and cv.CV_32FC2 type) in output image. 
For perspective transformation, you need a 3x3 transformation matrix. Straight lines will remain straight even after the transformation. To find this transformation matrix, you need 4 points on the input image and corresponding points on the output image. Among these 4 points, 3 of them should not be collinear. Then transformation matrix can be found by the function cv.getPerspectiveTransform. Then apply cv.warpPerspective with this 3x3 transformation matrix.
We use the functions: cv.warpPerspective (src, dst, M, dsize, flags = cv.INTER_LINEAR, borderMode = cv.BORDER_CONSTANT, borderValue = new cv.Scalar())
src  input image. 
dst  output image that has the size dsize and the same type as src. 
Mat  3 × 3 transformation matrix(cv.CV_64FC1 type). 
dsize  size of the output image. 
flags  combination of interpolation methods (cv.INTER_LINEAR or cv.INTER_NEAREST) and the optional flag WARP_INVERSE_MAP, that sets M as the inverse transformation (𝚍𝚜𝚝→𝚜𝚛𝚌). 
borderMode  pixel extrapolation method (cv.BORDER_CONSTANT or cv.BORDER_REPLICATE). 
borderValue  value used in case of a constant border; by default, it is 0. 
cv.getPerspectiveTransform (src, dst)
src  coordinates of quadrangle vertices in the source image. 
dst  coordinates of the corresponding quadrangle vertices in the destination image. 